Energy absorbing beams, such as leaf springs, are well known in the art. The design of a multiple-leaf spring, such as used in the automobile industry, is a highly specialized art combining both theory and experiment. See Virgil Moring Aires, Design of Machine Elements, 3d ed., pp. 189-195, The MacMillan Co., New York, 1955.
Flat and curved springs are basically beams whose stresses and deflections can be calculated using the ordinary beam equations. These springs, however, are inefficient in their use of material because of the fact that the stress is not constant throughout the beam. A better arrangement of material, from the consideration of stress, is to design the beam with a triangular shape. That is, the width of the beam may be decreased as the beam extends from its point of support to its outermost tip, assuming the beam is a cantilevered beam; or, in place of width, the thickness may be decreased from its point of support to the outermost tip.
As it is difficult to fabricate beams having such cross-sectional variations, it is common to form the desired triangular shape by placing a plurality of flat leaf springs one on top of the other. Such a spring will have approximately the same stress as that of a triangularly configured beam. However, there are a number of considerations which contribute to inaccuracies or complexities in designing such a beam include the effect of friction between the leaves, the effect of stress concentration, the use of tapered ends on each leaf spring, and the added effect of U-bolts and clips utilized to clamp the plurality of flat or curved leaf springs into the desired shape. See Joseph E. Shigley, Machine Design, McGraw-Hill Series in Mechanical Engineering, 1st ed., pp. 236-238, The McGraw-Hill Co., Inc., New York, 1956.
From the consideration of steel leaf springs formed from a plurality of flat or curved steel plates, the art has advanced to the proposed utilization of glass polymeric resin springs which may be up to five times lighter than the steel leaf spring they replace. See an article by Gordon G. Warner and Ashod Torosian, "Glass/Epoxy Spring is 80% Lighter Than Steel," Plastic Design Forum, July/August, p. 14, 1980. In this article, various leaf springs are discussed including a leaf spring having a constant thickness with a varying triangular width and a leaf spring having a constant width with a parabolic thickness variation. Also discussed is another design approach which includes a constant area with a hyperbolic width variation. The article talks of replacing a 41 pound, 10-spring, steel beam with an 8 pound glass-epoxy spring that is designed with a constant area which, in theory, tapers to a zero thickness and infinite width. This design is nicknamed the "bow-tie" shape.
The Warner and Torosian article goes on to state that different manufacturing processes are available to obtain a maximum elastic-strain energy from material with continuous unidirectional fibers. Four processes are mentioned including: (1) pultrusion/compression molding; (2) prepreg laminate/compression molding; (3) wet-charge compression molding, and (4) filament winding. Pultrusion/compression molding is said to be capable of producing pieces having constant width and thickness which are suitable for conventional multi-leaf design. The article states that the prepreg (preimpregnated) laminate/compression molding process can produce a part with variable or constant thickness. However, preimpregnated filaments must be hand placed into a laminate layer within a mold. This manufacturing process is labor intensive and produces a discontinuous structure. The wet-charged compression molding process and the filament winding process described within the Warner and Torosian article is said to require a constant cross-sectional area. These methods thus restrict the leaf spring to either the hyperbolic-width (bow-tie) or conventional multileaf spring designs. Leaf springs manufactured by Warner and Torosian were by the filament winding process with a "bow-tie" constant area, design.
The designs discussed in the Warner and Torosian article are discussed further in an article entitled "FRP Halves Spring Weight, Improves Ride" Automotive Engineering, May, 1981, pp 31-36, based on SAE paper 810325, "Light Truck FRP Leaf Spring Development," by Terry N. Trebilcock and Joseph N. Epel. This article describes three types of leaf springs including a constant section spring; a constant width, tapered spring; and a constant area spring. The Trebilock and Epel article then goes on to state that constant width (variable area, variable thickness) spring poses manufacturing problems and discusses the constant area spring discussed in the Warner and Torosian article.